TY - JOUR
T1 - Nilpotent orbits and Whittaker functions for derived functor modules of Sp(2, ℝ)
AU - Miyazaki, Takuya
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2002/8
Y1 - 2002/8
N2 - We study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp (2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in g*ℝ and the asymptotic support of the cohomological representation.
AB - We study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp (2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in g*ℝ and the asymptotic support of the cohomological representation.
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U2 - 10.4153/CJM-2002-030-8
DO - 10.4153/CJM-2002-030-8
M3 - Article
AN - SCOPUS:0036687539
VL - 54
SP - 769
EP - 794
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
SN - 0008-414X
IS - 4
ER -